Couple of things I noticed while playing the game:

1.  Can't move with ASDW on my keyboard. Would improve usability to allow both arrow keys and ASDW
2. That third screen jump requires a bit too precise jump timing. Sometimes I'd get it on the first try, and breeze through the next few screens, other times the character would fly off, not jumping, and just fall to their death, which is a little frustrating after you're pretty sure you've got the timing down.
3. The similar jump to 3rd screen, but with spikes is even worse, because it's quite a bit farther along. After probably my 10th try at getting through the spikes on that last screen (I assume I was close to the end of the level bcz I'd opened a lot of doors), I just gave up. I'd lower the difficulty of this screen a bit. I don't think people are going to be willing to go through all the other screens just to die on that last spike jump 100 times just to have to start over and do it all over again.
4.  I can't quit the game properly, or seem to reset. Not sure if those don't work, or if I just wasn't in the right menu. But I had to exit the game using the windows key, and then x out from there.

I'd say work on polishing the jump mechanic a bit more. Otherwise, really great job on that Atari feel. The sound effects are spot on, the visuals are great. Over all nice job, looking forward to seeing more of this one.